Filter-tipped cigarettes are assembled into bundles each including a predetermined number of (e.g., 20) filter-tipped cigarettes, and the cigarette bundles are packaged by a packaging machine, such as the one disclosed in Patent Document 1, to produce cigarette packs. In the packaging machine disclosed in Patent Document 1, a wrapper is wrapped around a cigarette bundle comprised of multiple tiers of filter-tipped cigarettes arranged side by side with their axes paralleled, and then excess portions of the wrapper at its opposite open ends are folded inward to close the open ends, thereby packaging the cigarette bundle.